M7R0
I&hellot+6"F$F$F$C:-%&printG6#%GThis~is~the~Maple~program~"EigenMatch"G-F'6#%9V
ersion~of~June~14,~2018G-%'printfG6#Q"|+F$-F'6#%]oIt~accompanies~the~paper~"The
~perfect~matching~association~scheme"G-F'6#%8by~Murali~K.~SrinivasanG-F'6#%gnav
ailable~at~<http://www.math.iitb.ac.in/|irmks/papers/pm.pdf>GF--F'6#%fqThe~prog
ram~computes~the~eigenvalues~of~the~Bose-Mesner~algebra~of~the~perfect~matching
~association~schemesG-F'6#%hoProgram~notes~available~at~<http://www.math.iitb.a
c.in/|irmks/papers/eigen.pdf>G-F'6#%8Here~are~a~few~examplesGF--F'6#%dp1.~To~fi
nd~the~eigenvalue,~on~the~eigenspace~indexed~by~the~even~Young~diagram~[8,6,4,2
],G-F'6#%dpof~the~orbital~basis~element~of~B_20~indexed~by~the~even~partition~[
6,6,4,4],~please~typeG-F'6#%>thetahat([8,6,4,2],[6,6,4,4])GF--F'6#%dp2.~To~find
~the~eigenvalue,~on~the~eigenspace~indexed~by~the~even~Young~diagram~[8,6,4,2],
G-F'6#%jnof~the~perfect~matching~derangement~matrix~in~B_20,~please~typeG-F'6#%
2eigder([8,6,4,2])GF--F'6#%hp3.~To~find~the~entire~spectrum~of~the~perfect~matc
hing~derangement~matrix~in~B_20~please~typeG-F'6#%,specder(20)GF--F'6#%doFor~ot
her~procedures~and~the~actual~programs~please~see~the~program~notesG-%'RETURNGF
$F$F$F$6#""!F$,
I%parkt+6$%"nG%"kGF$6#%)rememberGF$C%@$5519$F[o19%F[o2FhoFjo-Fin6#F[o@$/Fho"""-
Fin6#F`p-Fin6#,&-F\o6$,&FhoF`p!""F`p,&FjoF`pFipF`pF`p-F\o6$,&FhoF`pFjoFipFjoF`p
F$F$F$6#""#F$,
I$part+6#F_oF$FaoF$-Fin6#-%$addG6$-F\o6$FhoF`o/F`o;F`pFhoF$F$F$6#F`pF$,
I%ppart+FbqF$FaoF$C$@$F_pFap-Fin6#,&F`pF`p-Ffq6$-F`q6#,&FhoF`p%"iGFip/Fir;F`pFh
pF`pF$F$F$6#F`pF$,
I(rankpart+6#%"LG6$F_oFirFaoF$C&>8$-Ffq6$&Fho6#8%/Fis;F`p-%%nopsG6#Fho@$/&FhoFb
pF`pFap@$/F\tF`p-Fin6#-F`q6#Fds-Fin6#,&-Ffq6$-F\o6$FdsFis/Fis;F`p,&FatF`pFipF`p
F`p-F]s6#-%'subsopG6$/F`p%%NULLGFhoF`pF$F$F$6#F`pF$,
I*unrankpart+6$%"rGF_o6$%"jG%"tGFaoF$C'@$F_p-Fin6#7#-%$seqG6$F`p/Fds;F`pFjo>Fds
F`p>Fis-F\o6$FjoFds?(F$F`pF`pF$2,&FisF`p-F\o6$Fjo,&FdsF`pF`pF`pF`pFhoC$>FdsFdw>
Fis,&FisF`pF]wF`p-Fin6#7$Fdw-%#opG6#-Fju6$,&FhoF`pFisFip,(FjoF`pFdsFipFipF`pF$F
$F$6#F_qF$,
I)rankppart+F_sFasFaoF$C%>FdsFes@$Fct-Fin6#-F]rFgt-Fin6#,&-Ffq6$-F`q6#,&FdsF`pF
isFip/Fis;F`p,&&Fho6#FipF`pFipF`pF`p-F]s6#-Feu6$/F\tFhuFhoF`pF$F$F$6#F`pF$,
I+unrankppart+F\vF^vFaoF$C(@$F_pFcv@$/Fho-F]r6#Fjo-Fin6#7#Fjo>FdsF`p>FisF[o?(F$
F`pF`pF$2,&FisF`p-F`q6#,&FjoF`pFdsFipF`pFhoC$>FisF^[l>FdsFdw-Fin6#7$-F]x6#-Fju6
$FaxFa[lFdsF$F$F$6#F_qF$,
I$cobt+F_s6$Fir%"SGFaoF$C&@$Fct-Fin6#7$FatFip>Fis-%$mapG6$t+6#%"xGF$6$%)operato
rG%&arrowGF$FhpF$F$F$6#F`p-F]\lFcu@$/Fat&Fho6#F_q-Fin6#7$Fat-F]x6#-Feu6$FguFis-
Fin6#7$Fat-F]xFhsF$F$F$6#F`pF$,
I'insertt+6$F`sF\]lF$F$F$C%@$/F\tF[oFgz@$1FatFjo-Fin6#7$Fjo-F]xF^t-Fin6#7$Fat-F
]x6#-Fb^l6$FduFjoF$F$F$6#F_qF$,
I,updatematcht+6%'F`s%&ArrayGF_o%"aG6(F`\l%"AGFirF_v%"uGF`oF$F$C&>Fis-Fj_l6$;F`
pFezt+6#FirF$F]]lF$F[oF$F$F$6#F`p?(8&F`pF`pFez%%trueGC&>Fds-F_z6$Fh`lFjo?(8'F`p
F`p,&-F]tFgtF`pFipF`pFi`lC$>8(-Fdx6#7$-F]x6#-Feu6$/F_alFhu-Feu6$/FaalFhuFds,&&F
ds6#F_alF`p&FdsFhyF`p>&Fis6#Fdalz'6%FablFebl&Fho6#Fh`l\[[[[[[[\[[[mF_q[[[[\[[[[
[[[lF`p>8)Fcbl?(F_alF`pF`p,&F\clF`pFipF`pFi`lC%>Fdal-Fdx6#7$-F]x6#-Fb^l6$F]bl,&
F\clF`pF_alFipF_al>Febl,&FiblF`pFeblF`p>&FisFjbl,&FiblF`pF\dlF`p?(Fh`lF`pF`pFez
Fi`l>F\dl,&F\dlF`p*&9&F`pFiblF`pFip-FinFhsF$F$F$6#""$F$,
I+updatepermt+Fh_lF\`lF$F$C&>Fis-Fj_l6$Fc`lt+Fe`lF$F]]lF$F[oF$F$F$6#F`p?(Fh`lF`
pF`pFezFi`lC&>FdsF\al?(F_alF`pF`pF`alFi`lC$>FdalFeal>Feblz'Fhbl\[[[[[[[\[[[mF`p
[[[[\[[[[[[[lF`p>F\clFcbl?(F_alF`pF`pF^clFi`lC$>FdalFacl>FeblFjcl?(Fh`lF`pF`pFe
zFi`l>F\dlF`dlFcdlF$F$F$6#FedlF$,
I'phirowt+F_s6,F_o%"mGF`\l%"RGFir%"JG%"FGF^`l%"TG%"vGFaoF$C0>Fds-Ffq6$&FhoFfbl/
FdalF[t@$/FdsF`p-Fin6#-Fj_l6$;F`pF`pF`p@%/FgyF`p>F\clF[z>F\cl7$-F]xFjyFfy>Fh`l-
F^fl6#F\cl>F_al-Fj_l6$;F`pF[yt+Fe`lF$F]]lF$F[oF$F$F$6#F`p?(FdalF`pF`p-F`q6#,&Fd
sF`pFipF`pFi`l>&F_alFfbl&Fh`lFfbl>8*-F]\lF\hl@%Fegl>F[il-Feu6$/-F]t6#F[ilFhuF[i
l>F[il-Feu6$/,&FbilF`pFipF`pFhuF[il?(FdalF`pF`pFbilFi`l>F_al-Ffdl6%F_alFds&F[il
Ffbl>8,-Fj_l6$;F`pFftt+Fe`lF$F]]lF$F[oF$F$F$6#F`p?(FdalF`pF`pF[yFi`lC%>8+-F_z6$
FdalFds>8--Fb^l6$-Feu6$/-F]t6#FhjlFhuFhjl&FhjlFhy>&F_jl6#-F]s6#F\[m,&FhhlF`pFf[
mF`p>Fis&F_jlFbp?(FdalF`pF`pFftFi`l>&F_jlFfbl*&F_\mF`pFisFip-Fin6#F_jlF$F$F$6#F
`pF$,
I)thetarowt+F_sF`flFaoF$C0>Fds,$Fifl#F`pF_q@$F^glF_gl@%/FgyF_q>F\clF[z>F\cl7$Fi
gl,&FgyF`p!"#F`p>Fh`l-Fd\mF\hl>F_al-Fj_l6$F`hlt+Fe`lF$F]]lF$F[oF$F$F$6#F`p?(Fda
lF`pF`pFdhlFi`l>FhhlFihl>F[ilF\il@%F\]m>F[ilF_il>F[ilFeil?(FdalF`pF`pFbilFi`l>F
_al-Ff_lF\jl>F_jl-Fj_l6$Fbjlt+Fe`lF$F]]lF$F[oF$F$F$6#F`p?(FdalF`pF`pF[yFi`lC%>F
hjlFijl>F\[mF][m>Ff[mFj[m>FisF\\m?(FdalF`pF`pFftFi`l>F_\mF`\mFa\mF$F$F$6#F`pF$,
I'eigdert+6#%'lambdaG6(F_oFaflFir%"eGFefl%#muGF$F$C(>Fis-Ffq6$Fibl/Fh`lF[t>Fds,
$FisFi\m>F_alF[o>Fdal-Fd\mF^t?(Fh`lF`pF`pFftFi`lC$>F\cl-Fju6$Fh`lFds@$2F`p&F\cl
Fhy>F_al,&F_alF`p&FdalFjblF`p-FinFbblF$F$F$6#F`pF$,
I(specdert+6#Fafl6%F_oFirF`sF$F$C$>Fds,$FhoFi\m?(FisF`pF`pFftFi`lC%>Fh`l-Fju6$F
isFds>Fh`l-Fh\l6$t+F[]lF$F]]lF$,$FhoF_qF$F$F$6#F`pFh`l-F.6%Qcq~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%a
~:~~%a|+|+F$Fh`l-F`_mFjblF$F$F$6#F`pF$,
I'phihatt+6$Fc_mFf_mF$F$F$-Fin6#&-F^flF^t6#-F]sFfzF$F$F$6#F_qF$,
I)thetahatt+FgbmF$F$F$-Fin6#&F``m6#-F]s6#-Fh\l6$t+F[]lF$F]]lF$FdamF$F$F$6#F`pFj
oF$F$F$6#F_qF$
